SOLUTION: what is the focus of the conic section 12x+y^2-14y+1=0

Question 772845: what is the focus of the conic section 12x+y^2-14y+1=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what is the focus of the conic section
12x+y^2-14y+1=0
complete the square
(y^2-14y+49)-49+1=-12x
(y^2-14y+49)-48=-12x
(y^2-7)^2=-12x+48
(y^2-7)^2=-12(x-4)
This is an equation of a parabola that opens leftward:
Its basic equation: (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex
For given parabola:
vertex: (4,7)
axis of symmetry: y=7
4p=12
p=3
focus: (1,7)
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